Effect of photon propagation on a near-zero-refractive-index medium

We present a model describing the transmission of light through atomic media with a vanishing index of refraction. Zero-index materials are of particular interest as the infinite phase velocity of light within the material offers the potential to manipulate electromagnetic waves to mediate dipole-dipole interactions over extended distances. We focus on the preparation of near-zero-index (NZI) conditions based on atomic coherence using two distinct atomic media as exemplary of generic NZI materials. We establish a model based on the Maxwell-Bloch equations to describe the propagation of a light pulse through these media. To investigate the sustainability of NZI under minimal light conditions, we assume single-photon intensity of the propagating pulse. Specifically, we examine whether the spatial phase change of the photon remains near zero as it traverses the medium. We employ a finite-element numerical approach to solve the coupled Maxwell-Bloch equations describing the photon propagation. Our results indicate that the presence of a photon within the medium will disrupt the NZI state, thus disallowing the establishment of enhanced dipole-dipole interactions over large distances.